Question

A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca's doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with μ= 140+# mg/dl and σ = #+1 mg/dl, where # is the last digit of your GCU student ID number. Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured:

1. Once?
2. 8 times?
3. 10 times?

Comment on the relationship between the probabilities observed in (a), (b), and (c).

Answer 1

Let the last digit of your GCU student ID number = 5 (change it)

The glucose level is Normal distribution with

mean = 140 + 5 = 145

standard deviation = 5 + 1 = 6

1)

Answer:

Probability = 0.7977

Explanation:

The probability is obtained by calculating the z score,

The probability is obtained from the z distribution table. In excel use function =1-NORM.S.DIST(-0.8333,TRUE)

2)

Answer:

Probability = 0.9908

Explanation:

sample size = 8

The sampling distribution of the sample mean will follow a normal distribution with

sample mean = 145

sample standard deviation = 6/sqrt(8)

The probability is obtained by calculating the z score,

3)

Answer:

Probability = 0.9958

Explanation:

sample size = 10

The sampling distribution of the sample mean will follow a normal distribution with

sample mean = 145

sample standard deviation = 6/sqrt(10)

The probability is obtained by calculating the z score,

4)

Conclusion: From the calculated probabilities we can see that as the sample size increases, the probability that the glucose level is above the average value also increases.